3y(y+6)=21

Solution for 3y(y+6)=21 equation:

Simplifying
3y(y + 6) = 21

Reorder the terms:
3y(6 + y) = 21
(6 * 3y + y * 3y) = 21
(18y + 3y2) = 21

Solving
18y + 3y2 = 21

Solving for variable 'y'.

Reorder the terms:
-21 + 18y + 3y2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 18y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 6y + y2) = 0

Factor a trinomial.
3((-7 + -1y)(1 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1y = 0 + -1
-1y = 0 + -1

Combine like terms: 0 + -1 = -1
-1y = -1

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Solution
y = {-7, 1}